PERLNUMBER(1) Perl Programmers Reference Guide PERLNUMBER(1) #
PERLNUMBER(1) Perl Programmers Reference Guide PERLNUMBER(1)
NNAAMMEE #
perlnumber - semantics of numbers and numeric operations in Perl
SSYYNNOOPPSSIISS #
$n = 1234; # decimal integer
$n = 0b1110011; # binary integer
$n = 01234; # octal integer
$n = 0x1234; # hexadecimal integer
$n = 12.34e-56; # exponential notation
$n = "-12.34e56"; # number specified as a string
$n = "1234"; # number specified as a string
DDEESSCCRRIIPPTTIIOONN #
This document describes how Perl internally handles numeric values.
Perl's operator overloading facility is completely ignored here.
Operator overloading allows user-defined behaviors for numbers, such as
operations over arbitrarily large integers, floating points numbers with
arbitrary precision, operations over "exotic" numbers such as modular
arithmetic or p-adic arithmetic, and so on. See overload for details.
SSttoorriinngg nnuummbbeerrss Perl can internally represent numbers in 3 different ways: as native integers, as native floating point numbers, and as decimal strings. Decimal strings may have an exponential notation part, as in “12.34e-56”. _N_a_t_i_v_e here means “a format supported by the C compiler which was used to build perl”.
The term "native" does not mean quite as much when we talk about native
integers, as it does when native floating point numbers are involved.
The only implication of the term "native" on integers is that the limits
for the maximal and the minimal supported true integral quantities are
close to powers of 2. However, "native" floats have a most fundamental
restriction: they may represent only those numbers which have a
relatively "short" representation when converted to a binary fraction.
For example, 0.9 cannot be represented by a native float, since the
binary fraction for 0.9 is infinite:
binary0.1110011001100...
with the sequence 1100 repeating again and again. In addition to this
limitation, the exponent of the binary number is also restricted when it
is represented as a floating point number. On typical hardware, floating
point values can store numbers with up to 53 binary digits, and with
binary exponents between -1024 and 1024. In decimal representation this
is close to 16 decimal digits and decimal exponents in the range of
-304..304. The upshot of all this is that Perl cannot store a number
like 12345678901234567 as a floating point number on such architectures
without loss of information.
Similarly, decimal strings can represent only those numbers which have a
finite decimal expansion. Being strings, and thus of arbitrary length,
there is no practical limit for the exponent or number of decimal digits
for these numbers. (But realize that what we are discussing the rules
for just the _s_t_o_r_a_g_e of these numbers. The fact that you can store such
"large" numbers does not mean that the _o_p_e_r_a_t_i_o_n_s over these numbers will
use all of the significant digits. See "Numeric operators and numeric
conversions" for details.)
In fact numbers stored in the native integer format may be stored either
in the signed native form, or in the unsigned native form. Thus the
limits for Perl numbers stored as native integers would typically be
-2**31..2**32-1, with appropriate modifications in the case of 64-bit
integers. Again, this does not mean that Perl can do operations only
over integers in this range: it is possible to store many more integers
in floating point format.
Summing up, Perl numeric values can store only those numbers which have a
finite decimal expansion or a "short" binary expansion.
NNuummeerriicc ooppeerraattoorrss aanndd nnuummeerriicc ccoonnvveerrssiioonnss As mentioned earlier, Perl can store a number in any one of three formats, but most operators typically understand only one of those formats. When a numeric value is passed as an argument to such an operator, it will be converted to the format understood by the operator.
Six such conversions are possible:
native integer --> native floating point (*)
native integer --> decimal string
native floating_point --> native integer (*)
native floating_point --> decimal string (*)
decimal string --> native integer
decimal string --> native floating point (*)
These conversions are governed by the following general rules:
• If the source number can be represented in the target form, that
representation is used.
• If the source number is outside of the limits representable in the
target form, a representation of the closest limit is used. (_L_o_s_s _o_f
_i_n_f_o_r_m_a_t_i_o_n)
• If the source number is between two numbers representable in the
target form, a representation of one of these numbers is used. (_L_o_s_s
_o_f _i_n_f_o_r_m_a_t_i_o_n)
• In "native floating point --> native integer" conversions the
magnitude of the result is less than or equal to the magnitude of the
source. (_"_R_o_u_n_d_i_n_g _t_o _z_e_r_o_"_.)
• If the "decimal string --> native integer" conversion cannot be done
without loss of information, the result is compatible with the
conversion sequence "decimal_string --> native_floating_point -->
native_integer". In particular, rounding is strongly biased to 0,
though a number like "0.99999999999999999999" has a chance of being
rounded to 1.
RREESSTTRRIICCTTIIOONN: The conversions marked with "(*)" above involve steps
performed by the C compiler. In particular, bugs/features of the
compiler used may lead to breakage of some of the above rules.
FFllaavvoorrss ooff PPeerrll nnuummeerriicc ooppeerraattiioonnss Perl operations which take a numeric argument treat that argument in one of four different ways: they may force it to one of the integer, floating, or string formats; or they may behave differently depending on the format of the operand. Forcing a numeric value to a particular format does not change the number stored in the value.
All the operators which need an argument in the integer format treat the
argument as in modular arithmetic, e.g., "mod 2**32" on a 32-bit
architecture. "sprintf "%u", -1" therefore provides the same result as
"sprintf "%u", ~0".
Arithmetic operators
The binary operators "+" "-" "*" "/" "%" "==" "!=" ">" "<" ">=" "<="
and the unary operators "-" "abs" and "--" will attempt to convert
arguments to integers. If both conversions are possible without loss
of precision, and the operation can be performed without loss of
precision then the integer result is used. Otherwise arguments are
converted to floating point format and the floating point result is
used. The caching of conversions (as described above) means that the
integer conversion does not throw away fractional parts on floating
point numbers.
++ "++" behaves as the other operators above, except that if it is a
string matching the format "/^[a-zA-Z]*[0-9]*\z/" the string
increment described in perlop is used.
Arithmetic operators during "use integer"
In scopes where "use integer;" is in force, nearly all the operators
listed above will force their argument(s) into integer format, and
return an integer result. The exceptions, "abs", "++" and "--", do
not change their behavior with "use integer;"
Other mathematical operators
Operators such as "**", "sin" and "exp" force arguments to floating
point format.
Bitwise operators
Arguments are forced into the integer format if not strings.
Bitwise operators during "use integer"
forces arguments to integer format. Also shift operations internally
use signed integers rather than the default unsigned.
Operators which expect an integer
force the argument into the integer format. This is applicable to
the third and fourth arguments of "sysread", for example.
Operators which expect a string
force the argument into the string format. For example, this is
applicable to "printf "%s", $value".
Though forcing an argument into a particular form does not change the
stored number, Perl remembers the result of such conversions. In
particular, though the first such conversion may be time-consuming,
repeated operations will not need to redo the conversion.
AAUUTTHHOORR #
Ilya Zakharevich "ilya@math.ohio-state.edu"
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>
SSEEEE AALLSSOO #
overload, perlop
perl v5.36.3 2023-02-15 PERLNUMBER(1)